/sci/ - Science & Math

Not sure if im retarded but cant figure this out.

I can do regular linear programming stuff with 2 variables however this question seems backwards as it is asking for an objective function and it has 3 decision variables which is confusing me.

What should be the thought process here? I can't think of how I should be making the objective function.
Since [math]x + y + 2z \leq 1[/math] is a plane so if the objective function intersects it it would make a line. But even then I'm kind of confused